The best way to think of classes is to think of them as the "Adventurer" job from FFV; that is, that they can pretty much equip almost any ability from any class(with a slight penalty to effectiveness), while Jobs are akin to loadouts from FPS like Battlefield in that you can equip them on the fly and gain specialized traits., and as others mentioned, you'll be gaining abilities through questing and such.

Example: Gladiator can pretty much DD or tank, and if need be you can specialize it further with enfeebles, healing or damaging magic depending on the situation. Equip the Paladin "loadout" and you're essentially "mega-tank" and gain whatever stat bonuses/abilities it comes with, but with the loss of cross classing abilities(to what extent we don't know I don't think). Unequip Paladin and you're back to your jack of all trades ol' Gladiator self.